GLMs for Car Insurance Pricing: Initial Policy Data Exploration
Mick Cooney mickcooney@gmail.com
2017-07-29
1 Introduction
This workbook performs the basic data exploration of the dataset.
dataexp_level_exclusion_threshold <- 100
dataexp_cat_level_count <- 40
dataexp_hist_bins_count <- 502 Load Data
First we load the dataset.
data(freMTPLfreq)
data(freMTPLsev)
policy_data_tbl <- freMTPLfreq
claim_data_tbl <- freMTPLsev %>%
group_by(PolicyID) %>%
summarise(claim_count = n()
,claim_total = sum(ClaimAmount)
)
rawdata_tbl <- policy_data_tbl %>%
left_join(claim_data_tbl, by = 'PolicyID') %>%
as_data_frame
glimpse(rawdata_tbl)## Observations: 413,169
## Variables: 12
## $ PolicyID <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19...
## $ ClaimNb <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ Exposure <dbl> 0.09, 0.84, 0.52, 0.45, 0.15, 0.75, 0.81, 0.05, 0.76, 0.34, 0.10,...
## $ Power <fctr> g, g, f, f, g, g, d, d, d, i, f, f, e, e, e, e, e, e, i, i, h, h...
## $ CarAge <int> 0, 0, 2, 2, 0, 0, 1, 0, 9, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ DriverAge <int> 46, 46, 38, 38, 41, 41, 27, 27, 23, 44, 32, 32, 33, 33, 33, 54, 6...
## $ Brand <fctr> Japanese (except Nissan) or Korean, Japanese (except Nissan) or ...
## $ Gas <fctr> Diesel, Diesel, Regular, Regular, Diesel, Diesel, Regular, Regul...
## $ Region <fctr> R72, R72, R31, R31, R52, R52, R72, R72, R31, R11, R24, R24, R11,...
## $ Density <int> 76, 76, 3003, 3003, 60, 60, 695, 695, 7887, 27000, 23, 23, 1746, ...
## $ claim_count <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...
## $ claim_total <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...2.1 Perform Quick Data Cleaning
### _TEMPLATE_
### Do simple datatype transforms and save output in data_tbl
data_tbl <- rawdata_tbl
names(data_tbl) <- data_tbl %>% names %>% clean_names
glimpse(data_tbl)## Observations: 413,169
## Variables: 12
## $ policy_id <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19...
## $ claim_nb <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ exposure <dbl> 0.09, 0.84, 0.52, 0.45, 0.15, 0.75, 0.81, 0.05, 0.76, 0.34, 0.10,...
## $ power <fctr> g, g, f, f, g, g, d, d, d, i, f, f, e, e, e, e, e, e, i, i, h, h...
## $ car_age <int> 0, 0, 2, 2, 0, 0, 1, 0, 9, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ driver_age <int> 46, 46, 38, 38, 41, 41, 27, 27, 23, 44, 32, 32, 33, 33, 33, 54, 6...
## $ brand <fctr> Japanese (except Nissan) or Korean, Japanese (except Nissan) or ...
## $ gas <fctr> Diesel, Diesel, Regular, Regular, Diesel, Diesel, Regular, Regul...
## $ region <fctr> R72, R72, R31, R31, R52, R52, R72, R72, R31, R11, R24, R24, R11,...
## $ density <int> 76, 76, 3003, 3003, 60, 60, 695, 695, 7887, 27000, 23, 23, 1746, ...
## $ claim_count <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...
## $ claim_total <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...We want to replace missing values on the claim data with zeros, and also need to check consistency between the claim counts in both the policy and claim data sets. In the event of a discrepancy, we will go with the claim count from the claim data.
data_tbl <- data_tbl %>%
mutate(claim_count = ifelse(is.na(claim_count), 0, claim_count)
,claim_total = ifelse(is.na(claim_total), 0, claim_total)
)
data_tbl %>% filter(claim_count != claim_nb)## # A tibble: 0 x 12
## # ... with 12 variables: policy_id <int>, claim_nb <int>, exposure <dbl>, power <fctr>,
## # car_age <int>, driver_age <int>, brand <fctr>, gas <fctr>, region <fctr>,
## # density <int>, claim_count <dbl>, claim_total <dbl>data_tbl <- data_tbl %>%
select(-claim_nb)
data_tbl %>% glimpse## Observations: 413,169
## Variables: 11
## $ policy_id <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19...
## $ exposure <dbl> 0.09, 0.84, 0.52, 0.45, 0.15, 0.75, 0.81, 0.05, 0.76, 0.34, 0.10,...
## $ power <fctr> g, g, f, f, g, g, d, d, d, i, f, f, e, e, e, e, e, e, i, i, h, h...
## $ car_age <int> 0, 0, 2, 2, 0, 0, 1, 0, 9, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ driver_age <int> 46, 46, 38, 38, 41, 41, 27, 27, 23, 44, 32, 32, 33, 33, 33, 54, 6...
## $ brand <fctr> Japanese (except Nissan) or Korean, Japanese (except Nissan) or ...
## $ gas <fctr> Diesel, Diesel, Regular, Regular, Diesel, Diesel, Regular, Regul...
## $ region <fctr> R72, R72, R31, R31, R52, R52, R72, R72, R31, R11, R24, R24, R11,...
## $ density <int> 76, 76, 3003, 3003, 60, 60, 695, 695, 7887, 27000, 23, 23, 1746, ...
## $ claim_count <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ claim_total <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...2.2 Create Derived Variables
We now create derived features useful for modelling. These values are new variables calculated from existing variables in the data.
data_tbl <- data_tbl %>%
mutate(policy_id = as.character(policy_id))
glimpse(data_tbl)## Observations: 413,169
## Variables: 11
## $ policy_id <chr> "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "1...
## $ exposure <dbl> 0.09, 0.84, 0.52, 0.45, 0.15, 0.75, 0.81, 0.05, 0.76, 0.34, 0.10,...
## $ power <fctr> g, g, f, f, g, g, d, d, d, i, f, f, e, e, e, e, e, e, i, i, h, h...
## $ car_age <int> 0, 0, 2, 2, 0, 0, 1, 0, 9, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ driver_age <int> 46, 46, 38, 38, 41, 41, 27, 27, 23, 44, 32, 32, 33, 33, 33, 54, 6...
## $ brand <fctr> Japanese (except Nissan) or Korean, Japanese (except Nissan) or ...
## $ gas <fctr> Diesel, Diesel, Regular, Regular, Diesel, Diesel, Regular, Regul...
## $ region <fctr> R72, R72, R31, R31, R52, R52, R72, R72, R31, R11, R24, R24, R11,...
## $ density <int> 76, 76, 3003, 3003, 60, 60, 695, 695, 7887, 27000, 23, 23, 1746, ...
## $ claim_count <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ claim_total <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...2.3 Check Missing Values
Before we do anything with the data, we first check for missing values in the dataset. In some cases, missing data is coded by a special character rather than as a blank, so we first correct for this.
### _TEMPLATE_
### ADD CODE TO CORRECT FOR DATA ENCODING HEREWith missing data properly encoded, we now visualise the missing data in a number of different ways.
2.3.1 Univariate Missing Data
We first examine a simple univariate count of all the missing data:
row_count <- data_tbl %>% nrow
missing_univariate_tbl <- data_tbl %>%
summarise_all(funs(sum(is.na(.)))) %>%
gather('variable','missing_count') %>%
mutate(missing_prop = missing_count / row_count)
ggplot(missing_univariate_tbl) +
geom_bar(aes(x = fct_reorder(variable, -missing_prop), weight = missing_prop)) +
scale_y_continuous(labels = comma) +
xlab("Variable") +
ylab("Missing Value Proportion") +
theme(axis.text.x = element_text(angle = 90))
We remove all variables where all of the entries are missing
remove_vars <- missing_univariate_tbl %>%
filter(missing_count == row_count) %>%
.[['variable']]
lessmiss_data_tbl <- data_tbl %>%
select(-one_of(remove_vars))With these columns removed, we repeat the exercise.
missing_univariate_tbl <- lessmiss_data_tbl %>%
summarise_all(funs(sum(is.na(.)))) %>%
gather('variable','missing_count') %>%
mutate(missing_prop = missing_count / row_count)
ggplot(missing_univariate_tbl) +
geom_bar(aes(x = fct_reorder(variable, -missing_prop), weight = missing_prop)) +
scale_y_continuous(labels = comma) +
xlab("Variable") +
ylab("Missing Value Proportion") +
theme(axis.text.x = element_text(angle = 90))
To reduce the scale of this plot, we look at the top twenty missing data counts.
missing_univariate_top_tbl <- missing_univariate_tbl %>%
arrange(desc(missing_count)) %>%
top_n(n = 50, wt = missing_count)
ggplot(missing_univariate_top_tbl) +
geom_bar(aes(x = fct_reorder(variable, -missing_prop), weight = missing_prop)) +
scale_y_continuous(labels = comma) +
xlab("Variable") +
ylab("Missing Value Proportion") +
theme(axis.text.x = element_text(angle = 90))
2.3.2 Multivariate Missing Data
It is useful to get an idea of what combinations of variables tend to have variables with missing values simultaneously, so to construct a visualisation for this we create a count of all the times given combinations of variables have missing values, producing a heat map for these combination counts.
missing_plot_tbl <- rawdata_tbl %>%
mutate_all(funs(is.na)) %>%
mutate_all(funs(as.numeric)) %>%
mutate(label = do.call(paste0, (.))) %>%
group_by(label) %>%
summarise_all(funs(sum)) %>%
arrange(desc(label)) %>%
select(-label) %>%
mutate(rowid = do.call(pmax, (.))) %>%
gather('col','count', -rowid) %>%
mutate(Proportion = count / row_count
,rowid = round(rowid / row_count, 4)
)
ggplot(missing_plot_tbl) +
geom_tile(aes(x = col, y = as.factor(rowid), fill = Proportion), height = 0.8) +
scale_fill_continuous(labels = comma) +
scale_x_discrete(position = 'top') +
xlab("Variable") +
ylab("Missing Value Proportion") +
theme(axis.text.x = element_text(angle = 90))
This visualisation takes a little explaining.
Each row represents a combination of variables with simultaneous missing values. For each row in the graphic, the coloured entries show which particular variables are missing in that combination. The proportion of rows with that combination is displayed in both the label for the row and the colouring for the cells in the row.
2.4 Inspect High-level-count Categorical Variables
With the raw data loaded up we now remove obvious unique or near-unique variables that are not amenable to basic exploration and plotting.
coltype_lst <- create_coltype_list(data_tbl)
catvar_valuecount_tbl <- data_tbl %>%
summarise_at(coltype_lst$split$discrete
,function(x) length(unique(x))) %>%
gather('var_name', 'level_count') %>%
arrange(-level_count)
print(catvar_valuecount_tbl)## # A tibble: 5 x 2
## var_name level_count
## <chr> <int>
## 1 policy_id 413169
## 2 power 12
## 3 region 10
## 4 brand 7
## 5 gas 2row_count <- nrow(data_tbl)
cat(paste0("Dataset has ", row_count, " rows\n"))## Dataset has 413169 rowsNow that we a table of the counts of all the categorical variables we can automatically exclude unique variables from the exploration, as the level count will match the row count.
unique_vars <- catvar_valuecount_tbl %>%
filter(level_count == row_count) %>%
.[["var_name"]]
print(unique_vars)## [1] "policy_id"explore_data_tbl <- data_tbl %>%
select(-one_of(unique_vars))Having removed the unique identifier variables from the dataset, we may also wish to exclude categoricals with high level counts also, so we create a vector of those variable names.
highcount_vars <- catvar_valuecount_tbl %>%
filter(level_count >= dataexp_level_exclusion_threshold
,level_count < row_count) %>%
.[["var_name"]]
cat(paste0(highcount_vars, collapse = ', '))We now can continue doing some basic exploration of the data. We may also choose to remove some extra columns from the dataset.
### You may want to comment out these next few lines to customise which
### categoricals are kept in the exploration.
drop_vars <- c(highcount_vars)
if(length(drop_vars) > 0) {
explore_data_tbl <- explore_data_tbl %>%
select(-one_of(drop_vars))
cat(paste0(drop_vars, collapse = ', '))
}3 Univariate Data Exploration
Now that we have loaded the data we can prepare it for some basic data exploration. We first exclude the variables that are unique identifiers or similar, and tehen split the remaining variables out into various categories to help with the systematic data exploration.
coltype_lst <- create_coltype_list(explore_data_tbl)
print(coltype_lst)## $split
## $split$continuous
## [1] "exposure" "car_age" "driver_age" "density" "claim_count" "claim_total"
##
## $split$discrete
## [1] "power" "brand" "gas" "region"
##
##
## $columns
## exposure power car_age driver_age brand gas
## "continuous" "discrete" "continuous" "continuous" "discrete" "discrete"
## region density claim_count claim_total
## "discrete" "continuous" "continuous" "continuous"3.1 Logical Variables
Logical variables only take two values: TRUE or FALSE. It is useful to see missing data as well though, so we also plot the count of those.
logical_vars <- coltype_lst$split$logical
for(plot_varname in logical_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
na_count <- explore_data_tbl %>% .[[plot_varname]] %>% is.na %>% sum
explore_plot <- ggplot(explore_data_tbl) +
geom_bar(aes_(x = plot_varname)) +
xlab(plot_varname) +
ylab("Count") +
scale_y_continuous(labels = comma) +
ggtitle(paste0('Barplot of Counts for Variable: ', plot_varname
,' (', na_count, ' missing values)')) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
plot(explore_plot)
}3.2 Numeric Variables
Numeric variables are usually continuous in nature, though we also have integer data.
numeric_vars <- coltype_lst$split$continuous
for(plot_varname in numeric_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
plot_var <- explore_data_tbl %>% .[[plot_varname]]
na_count <- plot_var %>% is.na %>% sum
plot_var %>% summary %>% print
explore_plot <- ggplot(explore_data_tbl) +
geom_histogram(aes_string(x = plot_varname), bins = dataexp_hist_bins_count) +
geom_vline(xintercept = mean (plot_var, na.rm = TRUE), colour = 'red', size = 1.5) +
geom_vline(xintercept = median(plot_var, na.rm = TRUE), colour = 'green', size = 1.5) +
xlab(plot_varname) +
ylab("Count") +
scale_x_continuous(labels = comma) +
scale_y_continuous(labels = comma) +
ggtitle(paste0('Histogram Plot for Variable: ', plot_varname
,' (', na_count, ' missing values)')
,subtitle = '(red line is mean, green line is median)')
print(explore_plot)
}## --
## exposure
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00273 0.20000 0.54000 0.56109 1.00000 1.99000
## --
## car_age
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 3.00 7.00 7.53 12.00 100.00
## --
## driver_age
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 18.0 34.0 44.0 45.3 54.0 99.0
## --
## density
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2 67 287 1985 1410 27000
## --
## claim_count
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0000 0.0000 0.0392 0.0000 4.0000
## --
## claim_total
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 0 0 83 0 2036833
3.3 Categorical Variables
Categorical variables only have values from a limited, and usually fixed, number of possible values
categorical_vars <- coltype_lst$split$discrete
for(plot_varname in categorical_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
na_count <- explore_data_tbl %>% .[[plot_varname]] %>% is.na %>% sum
plot_tbl <- explore_data_tbl %>%
.[[plot_varname]] %>%
as.character %>%
fct_lump(n = dataexp_cat_level_count) %>%
fct_count
explore_plot <- ggplot(plot_tbl) +
geom_bar(aes(x = fct_reorder(f, -n), weight = n)) +
xlab(plot_varname) +
ylab("Count") +
scale_y_continuous(labels = comma) +
ggtitle(paste0('Barplot of Counts for Variable: ', plot_varname
,' (', na_count, ' missing values)')) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
plot(explore_plot)
}## --
## power
## --
## brand
## --
## gas
## --
## region
3.4 Date/Time Variables
Date/Time variables represent calendar or time-based data should as time of the day, a date, or a timestamp.
datetime_vars <- coltype_lst$split$datetime
for(plot_varname in datetime_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
plot_var <- explore_data_tbl %>% .[[plot_varname]]
na_count <- plot_var %>% is.na %>% sum
plot_var %>% summary %>% print
explore_plot <- ggplot(explore_data_tbl) +
geom_histogram(aes_string(x = plot_varname), bins = dataexp_hist_bins_count) +
xlab(plot_varname) +
ylab("Count") +
scale_y_continuous(labels = comma) +
ggtitle(paste0('Barplot of Dates/Times in Variable: ', plot_varname
,' (', na_count, ' missing values)'))
plot(explore_plot)
}4 Bivariate Data Exploration
We now move on to looking at bivariate plots of the data set.
4.1 Pairs Plots
Pairs plots area very useful way of getting a quick idea of the relationships between variables in a data set.
Unfortunately, they do not scale well. Too many rows (say more than 5,000) can slow down the rendering, and more than 10 columns can make the plots uninterpretable as each cell is too small.
The technique is useful, so to circumvent these issues we sample the dataset. We select random columns and rows, and make a pairs plot of the subset, repeating this process for a number of iterations.
dataexp_pairsplot_itercount <- 3
dataexp_pairsplot_colcount <- 5
dataexp_pairsplot_rowcount <- 5000
if(ncol(data_tbl) > dataexp_pairsplot_colcount ||
nrow(data_tbl) > dataexp_pairsplot_rowcount) {
### Ugly hack to work around current dplyr bug for mutate_if
if(any(sapply(explore_data_tbl, is.logical))) {
conv_tbl <- explore_data_tbl %>%
mutate_if(is.logical, as.factor)
} else {
conv_tbl <- explore_data_tbl
}
conv_tbl <- conv_tbl %>%
mutate_if(function(x) (is.character(x) || is.factor(x)) && !all(is.na(x))
,function(x) fct_lump(x, n = 9))
for(i in 1:dataexp_pairsplot_itercount) {
cat("--\n")
cat(paste0("Pairs plot iter: ", i, "\n"))
pairs_tbl <- conv_tbl %>%
create_ggpairs_tbl(sample_cols = dataexp_pairsplot_colcount
,sample_rows = dataexp_pairsplot_rowcount
)
cat(paste0("Columns: ", paste0(names(pairs_tbl), collapse = ', '), "\n"))
pairs_tbl %>%
ggpairs(cardinality_threshold = NULL
,lower = list(combo = wrap('facethist', bins = 25))
) %>%
print
}
} else {
ggpairs(data_tbl) %>% print
}## --
## Pairs plot iter: 1
## Columns: car_age, driver_age, gas, claim_count, claim_total
## --
## Pairs plot iter: 2
## Columns: exposure, power, gas, density, claim_count
## --
## Pairs plot iter: 3
## Columns: power, driver_age, brand, region, density
4.2 Facet Plots on Variables
We want to look at how the variables split on the logical variables as this is a very natural way to observe the data.
### _TEMPLATE_
facet_varname <- 'gas'
facet_count_max <- 3
facet_formula <- formula(paste0("~ as.factor(", facet_varname, ")"))4.2.1 Logical Variables
For logical variables we facet on barplots of the levels, comparing TRUE, FALSE and missing data.
logical_vars <- logical_vars[!logical_vars %in% facet_varname]
for(plot_varname in logical_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
filter_formula <- formula(paste0("~ !is.na(", plot_varname, ")"))
plot_tbl <- data_tbl %>% filter_(filter_formula)
facet_count <- plot_tbl %>%
.[[facet_varname]] %>%
unique %>%
length %>%
min(facet_count_max)
explore_plot <- ggplot(plot_tbl) +
geom_bar(aes_string(x = plot_varname)) +
facet_wrap(facet_formula, scales = 'free') +
xlab(plot_varname) +
ylab("Count") +
scale_y_continuous(labels = comma) +
ggtitle(paste0(facet_varname, '-Faceted Barplots for Variable: ', plot_varname)) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
plot(explore_plot)
}4.2.2 Numeric Variables
For numeric variables, we facet on histograms of the data.
for(plot_varname in numeric_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
filter_formula <- formula(paste0("~ !is.na(", plot_varname, ")"))
plot_tbl <- data_tbl %>% filter_(filter_formula)
facet_count <- plot_tbl %>%
.[[facet_varname]] %>%
unique %>%
length %>%
min(facet_count_max)
explore_plot <- ggplot(plot_tbl) +
geom_histogram(aes_string(x = plot_varname), bins = dataexp_hist_bins_count) +
facet_wrap(facet_formula, scales = 'free') +
xlab(plot_varname) +
ylab("Count") +
scale_x_continuous(labels = comma) +
scale_y_continuous(labels = comma) +
ggtitle(paste0(facet_varname, '-Faceted Histogram for Variable: ', plot_varname)) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
print(explore_plot)
}## --
## exposure
## --
## car_age
## --
## driver_age
## --
## density
## --
## claim_count
## --
## claim_total
4.2.3 Categorical Variables
We treat categorical variables like logical variables, faceting the barplots of the different levels of the data.
categorical_vars <- categorical_vars[!categorical_vars %in% facet_varname]
for(plot_varname in categorical_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
filter_formula <- formula(paste0("~ !is.na(", plot_varname, ")"))
plot_tbl <- data_tbl %>% filter_(filter_formula)
facet_count <- plot_tbl %>%
.[[facet_varname]] %>%
unique %>%
length %>%
min(facet_count_max)
explore_plot <- ggplot(plot_tbl) +
geom_bar(aes_string(x = plot_varname)) +
facet_wrap(facet_formula, scales = 'free') +
xlab(plot_varname) +
ylab("Count") +
scale_y_continuous(labels = comma) +
ggtitle(paste0(facet_varname, '-Faceted Histogram for Variable: ', plot_varname)) +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
plot(explore_plot)
}## --
## power
## --
## brand
## --
## region
4.2.4 Date/Time Variables
Like the univariate plots, we facet on histograms of the years in the dates.
for(plot_varname in datetime_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
filter_formula <- formula(paste0("~ !is.na(", plot_varname, ")"))
plot_tbl <- data_tbl %>%
filter_(filter_formula) %>%
mutate_(plot_vartmp = plot_varname) %>%
mutate(plot_var = year(plot_vartmp))
facet_count <- plot_tbl %>%
.[[facet_varname]] %>%
unique %>%
length %>%
min(facet_count_max)
explore_plot <- ggplot(plot_tbl) +
geom_bar(aes(x = plot_var)) +
facet_wrap(facet_formula, scales = 'free') +
xlab(plot_varname) +
ylab("Count") +
scale_y_continuous(labels = comma) +
ggtitle(paste0(facet_varname, '-Faceted Histogram for Variable: ', plot_varname))
plot(explore_plot)
}5 Multivariate Visualisation
Having looked at the pairs plots we also look at multivariate plots of all the data. We do this using techniques known as ‘multidimensional scaling’ or MDS.
Many of these techniques do not scale well beyond a few thousand data points, so we repeat our sampling trick as before and create multiple plots from these samples.
numeric_vars <- create_coltype_list(explore_data_tbl)$split$continuous5.1 Multidimensional Scaling
We start with classic multidimensional scaling, also called ‘principal coordinates analysis’, which is done in R via the function cmdscale.
mds_iter_count <- 4
mds_sample_count <- 2000
row_ids <- data_tbl %>%
select(one_of(numeric_vars)) %>%
complete.cases
### _TEMPLATE_
### Choosing the first variable in the categorical list by default. You probably
### want to change that.
colour_var <- 'power'
input_tbl <- data_tbl %>%
select(one_of(c(numeric_vars, colour_var))) %>%
filter(row_ids)
construct_mds_plot <- function(mds_tbl) {
num_mds_dist <- mds_tbl %>% select(one_of(numeric_vars)) %>% dist
num_mds <- cmdscale(num_mds_dist, k = 2, eig = TRUE)
mds_tbl <- mds_tbl %>%
mutate(mds_d1 = num_mds$points[,1]
,mds_d2 = num_mds$points[,2])
mds_plot <- ggplot(mds_tbl) +
geom_point(aes_string(x = 'mds_d1', y = 'mds_d2', colour = colour_var)) +
xlab("MDS Dim 1") +
ylab("MDS Dim 2")
return(mds_plot)
}
mds_lst <- create_sampled_output(input_tbl, construct_mds_plot, mds_sample_count, mds_iter_count)
for(i in 1:length(mds_lst)) {
cat("--\n")
cat(paste0("MDS plot iter: ", i, "\n"))
mds_lst[[i]] %>% print
}## --
## MDS plot iter: 1
## --
## MDS plot iter: 2
## --
## MDS plot iter: 3
## --
## MDS plot iter: 4
5.2 t-SNE Plots
One standard method for doing this is t-SNE, t-distributed Stochastic Neighbourhood Embedding. This algorithm is a type of dimensionality reduction - it constructs a lower-dimensional set of data from the original dataset by attempting the minimise the Kullback-Lieber divergence between the original and target datasets.
t-SNE requires unique datapoints, so to ensure we do not pass repeated rows at any point, we may add a small amount of noise to the numeric columns to ensure uniqueness - t-SNE is a probabilistic process so this should not affect our output very much.
As with previous methods, we take samples from larger datasets and plot outputs from multiple samples.
tsne_iter_count <- 4
tsne_sample_count <- 10000
row_ids <- data_tbl %>%
select(one_of(numeric_vars)) %>%
complete.cases
### _TEMPLATE_
### Choosing the first variable in the categorical list by default. You probably
### want to change that.
colour_var <- 'power'
input_tbl <- data_tbl %>%
select(one_of(c(numeric_vars, colour_var))) %>%
jitter_numeric_variables %>%
filter(row_ids)
construct_tsne_plot <- function(tsne_tbl) {
data_tsne <- Rtsne(tsne_tbl %>% select(one_of(numeric_vars)), theta = 0.9)
tsne_tbl$tsne_d1 <- data_tsne$Y[,1]
tsne_tbl$tsne_d2 <- data_tsne$Y[,2]
tsne_plot <- ggplot(tsne_tbl) +
geom_point(aes_string(x = 'tsne_d1', y = 'tsne_d2', colour = colour_var)
,size = 0.5) +
xlab("t-SNE Dim 1") +
ylab("t-SNE Dim 2")
return(tsne_plot)
}
tsne_lst <- create_sampled_output(input_tbl, construct_tsne_plot, tsne_sample_count, tsne_iter_count)
for(i in 1:length(tsne_lst)) {
cat("--\n")
cat(paste0("t-SNE plot iter: ", i, "\n"))
tsne_lst[[i]] %>% print
}## --
## t-SNE plot iter: 1
## --
## t-SNE plot iter: 2
## --
## t-SNE plot iter: 3
## --
## t-SNE plot iter: 4
6 Outlier Identification
Another important part of data exploration is the identification of possible outliers, and we approach this in multiple ways.
In keeping with the methodical approach we start with a univariate perspective, looking at each numerical variable by itself and plotting the values in the variable both with and without the outliers.
6.1 Univariate Outlier Plots
for(plot_varname in numeric_vars) {
cat("--\n")
cat(paste0(plot_varname, '\n'))
plot_var <- data_tbl %>% .[[plot_varname]]
outlier_point <- identify_univariate_outliers(plot_var)
no_outlier_vals <- plot_var[outlier_point]
all_plot <- ggplot() +
geom_histogram(aes(x = plot_var), bins = dataexp_hist_bins_count) +
xlab(plot_varname) +
ylab("Count") +
scale_x_continuous(labels = comma) +
scale_y_continuous(labels = comma) +
ggtitle("All Data") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
no_outlier_plot <- ggplot() +
geom_histogram(aes(x = no_outlier_vals), bins = dataexp_hist_bins_count) +
xlab(plot_varname) +
ylab("Count") +
scale_x_continuous(labels = comma) +
scale_y_continuous(labels = comma) +
ggtitle("No Outliers") +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
plot_grid(all_plot, no_outlier_plot, ncol = 2) %>% print
}## --
## exposure
## --
## car_age
## --
## driver_age
## --
## density
## --
## claim_count
## --
## claim_total
We use the above plots to decide if we need to remove certain extreme values from the dataset.
# We place basic logic for identifying univariate outliers here
#data_filt_tbl <- data_tbl %>% mutate(uni_outlier = ifelse(val > 100))